The Kerr-NUT-(A)dS family of vacuum spacetimes includes all stationary black holes with a spherical horizon topology
and arbitrary mass, angular momentum and NUT parameters.
Following [1]}, we set \(D = 2n + \varepsilon \) , where \(\varepsilon = 0\) 
for even \(D\)  and \(\varepsilon = 1\)  for odd \(D\) . The Kerr-NUT-(A)dS metric attains its most
symmetric form in canonical
coordinates \((x_{k}, \psi _{j})\) ,
\( ds^{2} = \sum _{k = 1}^{n} \left[ \frac{U_{k}}{X_{k}} dx_{k}^{2} +\frac{X_{k}}{U_{k}}\left( \sum _{j = 0}^{n-1} A_{k}^{(j)} d\psi _{j}\right)^{2}\right] -\varepsilon \frac{ \mathcal {A}^{(n - 1 + \varepsilon )}}{A^{(n)}}\left( \sum _{j = 0}^{n - 1 + \varepsilon } d\psi _{j}\right)^{2}.\) 
